Re: Meyer's Argument against Gödel's Theorem



LauLuna wrote:
On Aug 24, 6:18 am, jeffreykeg...@xxxxxxxxx wrote:

Note that "meta-mathematical" here means "appealing to notions of
truth outside of the formalism". Some schools of philosophy of
mathematics have claimed there is no such thing as informal
mathematical truth. Gödel disagreed, though here he's not coming out
and saying so directly.

Consider that the meta-math of a particular system can be formalized
in another system.

The meta-math of which could be formalized yet in another system,
the meta-math of which could be formalized yet in another system,
....
to infinity. It seems to be the case.

Nevertheless, it's true that Gödel believed human
reason can eventually prove any mathematical truth, a feat no correct
formal system can achieve.

How could a finite mortal being as human "prove _any_ mathematical truth"?
For example, could a human being prove the truth of GC, or of cGC, or the
truth of there's neither?


--
"To discover the proper approach to mathematical logic,
we must therefore examine the methods of the mathematician."
(Shoenfield, "Mathematical Logic")
.